Spoilers Off applies to Tearjerker pages. All spoilers are unmarked.
Oblomov's breakup with Olga. She realizes that her Pygmalion Plot is failing and she can't drag him around for the rest of their lives; but that doesn't mean she stops loving him. Oblomov accepts her decision, takes the blame entirely on himself and wants her to be happy.
Sachar's last scene. For most of the novel, he covers the comedy with his antics, but after spoiler: Oblomov dies, nobody needs a mouthy, clumsy servant so he becomes a bagger and stays in the city because he doesn't want to leave his grave.